This paper analyzes the cost of disinflation under real wage rigidities in a micro-founded New Keynesian model. Unlike Blanchard and Galí (2007) who carried out a similar analysis in a linearized framework, we take non-linearities into account. We show that the results change dramatically, both qualitatively and quantitatively, for the steady states and for the dynamic adjustment paths. In particular, a disinflation implies a prolonged slump without any need for real wage rigidities.